Question

Verify the algebraic identities by paper cutting and pasting method  ( + )2 = 2 + 2 + 2  ( − )2 = 2 + 2 − 2

Answer 1

Step-by-step explanation:

Area of the square PQRS on the white sheet paper.

(a+b)2 = (4+2)2 = 6 x 6 = 36 sq. units ……….(i)

Area of two coloured squares I and II

area of Ist square = a2 = 42 = 16 sq.units

area of IInd square = b2 = 22 = 4 sq.units

Area of two coloured rectangles III and IV = 2(a x b) = 2(4 x 2) = 16 sq. units

Now, total area of four quadrilaterals (calculated)

= a2 + b2 + 2(ab)

= 16+4+16

= 36 sq. units ……….(ii)

Area of square ABCD = Total area of four quadrilaterals = 36 sq. units

Equating (i) and (ii)

Area of square PQRS = Area of square ABCD

i.e., (a+b)2 = a2 + b2 + 2ab

Answer 2

Answer:

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